It hasn't been enough to move the needle.
Calvin Watkins of The Athletic reported the Cowboys' current offer on the table would pay him $20 million per season over six years. Lawrence, who initially requested $20 million annually in long-term talks, has moved his price point to $22.5 million per season.
"Right now, the best way to describe it is we're at an impasse," Cowboys executive vice president Stephen Jones said. "We're apart. But certainly optimistic. No one thinks more of DeMarcus Lawrence than we do. He represents what we want on our football team, in terms of the way he plays the game. He certainly plays it at a high level. We'll continue to chop wood."
The Cowboys gave Lawrence the $20.5 million franchise tag earlier this month. The two sides will have until July to work out a long-term deal, or Lawrence will have to play under the tag in 2019.
Lawrence, 26, has made the Pro Bowl each of the last two seasons. He recorded 42 tackles and 10.5 sacks in 2018 despite playing through a torn labrum in his shoulder. Watkins' report says Lawrence plans to delay surgery on his shoulder until he receives a long-term contract.
"We're going to continue to try to move the ball forward and see if there is some common ground we can find," Jones said. "I'm certainly not going to draw any lines in the sand, and we haven't. No bright lines so far. We've just been apart. Hopefully, we can continue to come up with some creative ways to maybe create some common ground."
The impasse could wind up becoming a worst-case Le'Veon Bell situation if the Cowboys aren't careful. Lawrence could sit out all of camp and preseason without undergoing surgery, then sign his tag and have to sit out most (if not all) of the regular season while recovering.
It's a doomsday tactic neither side would prefer to happen, but it's something to monitor as we get closer to the July deadline.